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Probabilistic Hesitant Fuzzy Taxonomy Method Based on Best–Worst-Method (BWM) and Indifference Threshold-Based Attribute Ratio Analysis (ITARA) for Multi-attributes Decision-Making

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Abstract

The probabilistic hesitant fuzzy set (PHFS) is an important extension of hesitant fuzzy set (HFS), which can more accurately describe the uncertainty of elements and can show more flexibility of decision maker (DM) in the process of decision-making. Taxonomy method is a useful tool for grading, classifying, and comparing different activities with respect to their advantages and utility degree from studied attributes. In this paper, a probabilistic hesitant fuzzy Taxonomy method based on Best–Worst-Method (BWM) and Indifference Threshold-based Attribute Ratio Analysis (ITARA) for multi-attributes decision-making (MADM) is presented. First, the definitions about PHFS and probabilistic hesitant fuzzy element (PHFE) are introduced, and some corresponding operations are given. Second, we adopt BWM to obtain subjective weights and ITARA approach to obtain objective weights, by combining the subjective weights and objective weights together; we can derive the final weights. Furthermore, we extend the Taxonomy method to the PHFS. Finally, an example of selecting research topic is given to illustrate the usefulness of our proposed method. Compared with other useful methods, the validity and superiority of our proposed method can be showed.

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Acknowledgements

This paper is supported by the National Natural Science Foundation of China (No. 71771140), Project of cultural masters and “the four kinds of a batch” talents, the Special Funds of Taishan Scholars Project of Shandong Province (No. ts201511045), Major bidding projects of National Social Science Fund of China (No. 19ZDA080).

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Authors and Affiliations

  1. School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan, 250014, Shandong, China

    Peide Liu, Yifan Wu & Ying Li

Authors
  1. Peide Liu
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  2. Yifan Wu
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  3. Ying Li
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Corresponding author

Correspondence to Peide Liu.

Appendix

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See Table 16.

Table 16 The summary of the notations
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Liu, P., Wu, Y. & Li, Y. Probabilistic Hesitant Fuzzy Taxonomy Method Based on Best–Worst-Method (BWM) and Indifference Threshold-Based Attribute Ratio Analysis (ITARA) for Multi-attributes Decision-Making. Int. J. Fuzzy Syst. 24, 1301–1317 (2022). https://doi.org/10.1007/s40815-021-01206-7

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